Existence and Uniqueness of Solutions: Example 1
Example: Suppose the differential equation satisfies the Existence and Uniqueness Theorem
for all values of y and t. Suppose and
are two solutions to this differential equation.
- What can you say about the behavior of the solution of the
solution y(t) satisfying the initial condition y(0)=1?
Hint: Draw the two solutions and .
- Address the behavior of y(t) as t approaches ,
and as t approaches .
- First let us draw the graphs of and .
Since we have , we deduce from the
Existence and Uniqueness Theorem that for all t, we have
In particular, y(t) has the line y=t as an oblique asymptote
which answers the second question.
We cannot predict that y(t) is an increasing function.
S.O.S MATHematics home page
Do you need more help? Please post your question on our
S.O.S. Mathematics CyberBoard.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour